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Laywine C.F., Mullen G.L. — Discrete Mathematics Using Latin Squares
Laywine C.F., Mullen G.L. — Discrete Mathematics Using Latin Squares

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Название: Discrete Mathematics Using Latin Squares

Авторы: Laywine C.F., Mullen G.L.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 164

Добавлена в каталог: 24.02.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
(t, m, s)-Nets      241—254
(t, m, s)-Nets and coding theory      250
(t, m, s)-Nets and error-correcting codes      250 254
(t, m, s)-Nets and MOLS      244—250 253 254
Affine geometries      161—166 171 173
Affine geometries, k-flats defined      161
Affine plant(s)      68—70
Affine plant(s), algebraic derivation      133—136
Affine plant(s), axioms, defining      131
Affine plant(s), defargueuaa      143—146
Affine plant(s), nondesarguesian      146—150
Affine plant(s), order or finite      132
Agrippa, C      17
Algebraic background      269—277
anova      188 201
Axial classes      289
Background, algebraic      269—277
Balanced incomplete block design      153
Bipartite graph      287
Bose      1938
Bose, equivalence      137
Brack (geometric) nets      247
Brack- Ryser theorem      152
Brouwer, table from      213 215 219 220 226
Bye-boards      182
Casanova, and magic squares      176
Cayley (multiplication) table      95 103
Cayley theorem      96
Characterizing graphs with Hamilton cycles, problem      106
Classes, axial      289
Codecs and latin squares      205—226
Codecs from MOFS      215 226
Codecs from MOLS      209—213
Codecs from orthogonal hypercubes      216
Codecs, binary      205
Codecs, constant weight      217 218
Codecs, error-correcting      123 205—226
Codecs, Golomb — Posner MDS      213 216 226
Codecs, linear      206
Codecs, maximum distance separable (MDS), defined      212 213
Codecs, nonlinear      208
Codecs, optimal      213—221
Codecs, projective      219 4
Codecs, q-ary      205
Codecs, rate of      208
Codecs, repetition, of length ft      209 210
Codecs, ternary      205
Codecs, two weight      219
Codecs, weight (wt)      207
Column effects      190
Commutative ring      270
Critical set(s)      231 238 239 293
Critical set(s), and $3\times3$ latin square      293
Critical set(s), minimal      231 238 239
Cryptology and latin squares      228—239
Cryptology and latin squares, ciphertexts      228
Cryptology and latin squares, cryptology, cryptography, and cryptoanalysis defined      228
Cryptology and latin squares, enciphering and deciphering      228
Cryptology and latin squares, multilevel      232
Cryptology and latin squares, secret sharing schemes      230—233
Cryptology and latin squares, shadows of secret key      230
Cryptology and latin squares, shares of secret key      230
Deficiency of a set of MOLS      33 122
Derangement      78
Desargues configuration      143—146
Desargues configuration, affine formulation      146
Desargues configuration, defined      143
Desargues theorem      144 145
Desarguesian plane(s)      172
Desarguesian set of MOLS      22 35
Desarguesian set of MOLS, construction ot      21 22
Designs, affine resolvable      155 171—173
Designs, balanced incomplete block      153—155
Designs, resolvable      155
Designs, symmetric      155
Designs, transversal      27—32 37
Digital signature      237
Discordant permutation      77
Discrete logarithm cryptosystems      234—239
Discrete logarithm cryptosystems and Euler's function p      237 271
Discrete logarithm cryptosystems, no-key      236 237
Discrete logarithm cryptosystems, public-key      237 238
Discrete logarithm cryptosystems, RSA (Rivest, Shamir, and Adleman)      237—240
Discrete logarithm cryptosystems, three pass system      236 237
Discrete logarithm problem      103 234 239
Division algorithm      269
Duerer, Melencolia I engraving      17
Elementary intervals      242 243
Error-correcting codes      (see Code(s) error-correcting)
Euclidean plane(s)      131 133 136 143
Euler 36-officer problem      5—8 11 23 58 64 67 101 104 122 127 188
Euler bound      58—60
Euler circuit      119 120
Euler conjecture      8 23 26 27 37 8 101 104
Euler solution of Kdnigsberg bridge problem      106 127
Fermat last theorem      106
Fermat primes      291
Fields and irreducible polynomials      272 273 277 278 280
fields, defined      270
Fields, finite      271 278
Fields, Galois      273
Fields, properties of      274
Finite field      20 21 270—274 278
Finite field, primitive elements      274 277 291
Four color problem      106 126
Fractional replication plains)      226
Frequency square(s)      63—70
Frequency square(s) constant frequency      64
Frequency square(s) defined      63
Frequency square(s) nonconstant frequency      70
Frequency square(s) orthogonal sets of      63 64
Galois field      273
Generalized orthogonal array      251
Generator matrices      214—217 292
Geometric (Brack) nets      247
Geometric hypercubes, defined      163
Golf design      13
Graphs (and latin squares)      106—128
Graphs (and latin squares), 1-factor(ization)      107 126 286 287
Graphs (and latin squares), adjacency matrix      112
Graphs (and latin squares), bipartite      107 126
Graphs (and latin squares), edges      106
Graphs (and latin squares), monochromatic 1-factor      107
Graphs (and latin squares), net      122 126
Graphs (and latin squares), pseudo-net      122
Graphs (and latin squares), regular      121
Graphs (and latin squares), strongly regular      121—123
Graphs (and latin squares), vertices      106
Groups (and latin squares)      94—104
Groups (and latin squares), abelian      94
Groups (and latin squares), associative      94
Groups (and latin squares), commutative      94
Groups (and latin squares), cyclic      94
Groups (and latin squares), defined      94
Groups (and latin squares), examples of      94
Groups (and latin squares), finite      94
Groups (and latin squares), generator      94
Groups (and latin squares), identity element      94
Groups (and latin squares), inverse element      94
Groups (and latin squares), order n      94
Groups (and latin squares), properties of      94
Hall marriage theorem      108 109 287
Hall plane(s)      146 147 151 172
Hamilton circuit(s)      118 119 126 287
Hamilton cycles, characterizing graphs with      106
Hamiltonian path      115 116 126 287
Hamming (sphere-packing) bound      211 224
Hamming distance      206 226 257
Hohler definition of orthogonality      61
Howell master sheets      182 (see also Room squares)
Hughes polynomials      151 152
Hypercube(s) algorithm for construction from latin squares      294
Hypercube(s) d-dimensional      43
Hypercube(s) from latin squares      294
Hypercube(s) geometric, defined      163
Hypercube(s) latin      43 44
Hypercube(s) nonlatin      44
Hyperplanes      171—173
Hyperrectangles      70
Integers ring of, modulo n      270
Integers, congruent modulo n      269
Intervals, elementary      242 243
Irreducible polynomials      272 273 277 278 280
Kdnigsberg bridge problem      106 127
Knut-Vik designs (pandiagonal latin squares)      179
Kronecker product and hypercubes      57 58
Kronecker product and MOLS      23—27 124 125 280—282
Lagrange interpolation formula      20 274 296
Lagrange interpolation formula and polynomial representation      274
Lagrange theorem      38
Latin rectangle      15 93
Latin rectangle, first row      75 90 91
Latin rectangle, second row      75 84 85
Latin rectangle, third row      85—90
Latin square(s) and geometry      13 14
Latin square(s) and graphs      106—128
Latin square(s) and groups      94—104
Latin square(s) and linear algebra      14
Latin square(s) and statistics.      188—204
Latin square(s) applications      255—265
Latin square(s) applications, agricultural experiments      9—11
Latin square(s) applications, authentication schemes      263 264
Latin square(s) applications, check character systems      263 264
Latin square(s) applications, classic squares and broadcast squares      259 260 264
Latin square(s) applications, code design      11 12 101 102 228—239 263—265
Latin square(s) applications, committee formation      8 9
Latin square(s) applications, compiler testing.      263 265
Latin square(s) applications, cryptography      101 102 205—226 228—239 263—265
Latin square(s) applications, drug test design      11
Latin square(s) applications, experimental design      9—11 264
Latin square(s) applications, golf design      13 262
Latin square(s) applications, hash functions      263 264
Latin square(s) applications, network testing systems      263—265
Latin square(s) applications, tomography      263 265
Latin square(s) applications, tournament design      12 13 260—262
Latin square(s) column complete      115
Latin square(s) complete      115
Latin square(s) defined      3
Latin square(s) diagonal      36
Latin square(s) disjoint transversals      33 36
Latin square(s) generalized      257 264
Latin square(s) idempotent      33 34 36 123 124 282
Latin square(s) introduction to      3—17
Latin square(s) nearly consecutive symbols      263
Latin square(s) order n      279
Latin square(s) orthogonal      5—9 280 281
Latin square(s) orthogonal mates      32 33 36
Latin square(s) orthogonal sets      18 36 37
Latin square(s) orthogonal, pair of      21
Latin square(s) partial      14 15
Latin square(s) perfect      258 264
Latin square(s) perfect and conflict-free access to parallel memories      264
Latin square(s) perfect, main subsquare.      258
Latin square(s), r-orthogonal      257 264
Latin square(s), reduced      4 15 112 113 126
Latin square(s), row      97—100 285
Latin square(s), row complete, II      115 126
Latin square(s), self-orthogonal      33 38 39 282
Latin square(s), symmetric idempotent      13
Latin square(s), transversals of.      36 37
Latin square(s), unipotent      112 113
Loops      97
MacNeish's conjecture      26 27 37
Magic cube      291
Magic squares      175—181 290
Magic squares, 3-dimensional      180
Magic squares, 3-dimensional perfect      180
Magic squares, addition-multiplication      179 180
Magic squares, applications of      175
Magic squares, defined      175
Magic squares, multiplicative properties      181
Magic squares, order      7 181
Manage numbers      86 90 91 93
Melencotia I      175 176
Menage problem      86—89 93
Menage problem, enumeration of 3-row latin rectangles      93
Mersenne primes      291
Moebius inversion      93
MOFS      (see Mutually orthogonal frequency squares)
MOHC      (see Mutually orthogonal hypercubes)
MOLS      (see Mutually orthogonal latin squares)
Monte Carlo methods      253
MOPLS      (see Mutually orthogonal partial latin squares)
Moschopoulos, E      175
Multiplication (Cayley) table      95 103
Mutually orthogonal frequency squares (MOFS)      64—70 284 288
Mutually orthogonal frequency squares (MOFS), complete set      64
Mutually orthogonal frequency squares (MOFS), construction by substitution      66—70
Mutually orthogonal frequency squares (MOFS), nonconstant frequency      70
Mutually orthogonal frequency squares (MOFS), polynomial construction      64—66
Mutually orthogonal hypercubes (MOHC)      43—62 247—254 288 289 294
Mutually orthogonal hypercubes (MOHC) and affine designs      153—173
Mutually orthogonal hypercubes (MOHC), blocks      153 171 172
Mutually orthogonal hypercubes (MOHC), complete set      51
Mutually orthogonal hypercubes (MOHC), composition      153
Mutually orthogonal hypercubes (MOHC), defined      44
Mutually orthogonal hypercubes (MOHC), higher orthogonality      250—252
Mutually orthogonal hypercubes (MOHC), Hohler orthogonality      61
Mutually orthogonal hypercubes (MOHC), MacNeish construction      57 58
Mutually orthogonal hypercubes (MOHC), order      6 58 59
Mutually orthogonal hypercubes (MOHC), polynomial construction      47—51 248
Mutually orthogonal hypercubes (MOHC), recursive construction      51—57 61 249 250
Mutually orthogonal hypercubes (MOHC), type      44
Mutually orthogonal Latin squares (MOLS)      18—39 280—282 285 292 294
Mutually orthogonal latin squares (MOLS), and Kronecker product      280 281
Mutually orthogonal latin squares (MOLS), applications      18 37
Mutually orthogonal latin squares (MOLS), complete set      20
Mutually orthogonal latin squares (MOLS), deficiency of a set      33
Mutually orthogonal latin squares (MOLS), defined      19
Mutually orthogonal latin squares (MOLS), Desarguesian construction      21 22
Mutually orthogonal latin squares (MOLS), Desarguesian set      22 35
Mutually orthogonal latin squares (MOLS), isomorphic sets      22 34
Mutually orthogonal latin squares (MOLS), maximum number      19
Mutually orthogonal latin squares (MOLS), nondesarguesian      146 147
Mutually orthogonal latin squares (MOLS), nonisomorphic sets      22
Mutually orthogonal latin squares (MOLS), nonprime power sets      23 24
Mutually orthogonal latin squares (MOLS), polynomial representation      20 21
Mutually orthogonal latin squares (MOLS), power set of      35 36
Mutually orthogonal latin squares (MOLS), prime power sets of      20 21
Mutually orthogonal latin squares (MOLS), sets of nonisomorphic      280
Mutually orthogonal partial latin squares (MOPLS)      255—257 264
Mutually orthogonal partial latin squares (MOPLS), application to computer databases      256 257
Mutually orthogonal partial latin squares (MOPLS), Nets      293—295
Mutually orthogonal partial latin squares (MOPLS), p-compatible      255
Numerical integration      241 242 253
One-way analysis of variance (ANOVAX      188 201
Order, definitions of      102
orthogonal arrays      31 32 36 37 197 246 247 280 281 294
Orthogonal arrays, equivalent objects      31 32
Orthogonal arrays, generalized      251
Orthogonal hypercubes      (see Mutually orthogonal hypercubes)
Orthogonal latin square graph (OLSG)      123—126
Orthogonality, Hohler’s definition of      61
Pairwise orthogonal squares      19
Pandiagonal latin squares (Knut-Vik designs)      179
Partial latin square(s)      230 238 239
Permutation cube(s)      43 223 224—226
Permutation cube(s) reduced      224 225
Permutation(s), theory of      95 96
Perspective triangles      143—146
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